# ForecastCompIsocurv

We forecast constraints on the **variance of the amplitude of compensated isocurvature perturbations** based on the second order effect on the CMB power spectrum. Details can be found here: http://arxiv.org/pdf/1511.04441v2.pdf

Brief overview:

We parametrize the effect of a sky-varying CIP as

We expand the amplitude of the compensated isocurvature perturbations in spherical harmonics as

, and the CIP angular power spectrum is given by

Our constraints are on the variance of the CIP amplitude, , which can be expressed in terms of the CIP power spectrum as

The observable signature is the second order effect on the CMB power spectrum

Results:

Using Planck, our best constraint is:

With S4, we can reach up to an order of magnitude improvement:

- S4 forecast as a function of sensitivity and beam size: File:S4CIPsNoise.pdf

- S4 forecast as a function of the sky coverage: File:S4CIPsfsky.pdf